{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "spare-cycling",
   "metadata": {},
   "source": [
    "# 习题 4.6\n",
    "\n",
    "![习题 4.6](https://tva1.sinaimg.cn/large/008i3skNly1gra4yo6us3j31n40bgah5.jpg)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "athletic-doctrine",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A data.frame: 49 × 6</caption>\n",
       "<thead>\n",
       "\t<tr><th scope=col>x1</th><th scope=col>x2</th><th scope=col>x3</th><th scope=col>y1</th><th scope=col>y2</th><th scope=col>y3</th></tr>\n",
       "\t<tr><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th><th scope=col>&lt;int&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><td> 60</td><td> 69</td><td> 62</td><td> 97</td><td> 69</td><td> 98</td></tr>\n",
       "\t<tr><td> 56</td><td> 53</td><td> 84</td><td>103</td><td> 78</td><td>107</td></tr>\n",
       "\t<tr><td> 80</td><td> 69</td><td> 76</td><td> 66</td><td> 99</td><td>130</td></tr>\n",
       "\t<tr><td> 55</td><td> 80</td><td> 90</td><td> 80</td><td> 85</td><td>114</td></tr>\n",
       "\t<tr><td> 62</td><td> 75</td><td> 68</td><td>116</td><td>130</td><td> 91</td></tr>\n",
       "\t<tr><td> 74</td><td> 64</td><td> 70</td><td>109</td><td>101</td><td>103</td></tr>\n",
       "\t<tr><td> 64</td><td> 71</td><td> 66</td><td> 77</td><td>102</td><td>130</td></tr>\n",
       "\t<tr><td> 73</td><td> 70</td><td> 64</td><td>115</td><td>110</td><td>109</td></tr>\n",
       "\t<tr><td> 68</td><td> 67</td><td> 75</td><td> 76</td><td> 85</td><td>119</td></tr>\n",
       "\t<tr><td> 69</td><td> 82</td><td> 74</td><td> 72</td><td>133</td><td>127</td></tr>\n",
       "\t<tr><td> 60</td><td> 67</td><td> 61</td><td>130</td><td>134</td><td>121</td></tr>\n",
       "\t<tr><td> 70</td><td> 74</td><td> 78</td><td>150</td><td>158</td><td>100</td></tr>\n",
       "\t<tr><td> 66</td><td> 74</td><td> 78</td><td>150</td><td>131</td><td>142</td></tr>\n",
       "\t<tr><td> 83</td><td> 70</td><td> 74</td><td> 99</td><td> 98</td><td>105</td></tr>\n",
       "\t<tr><td> 68</td><td> 66</td><td> 90</td><td>119</td><td> 85</td><td>109</td></tr>\n",
       "\t<tr><td> 78</td><td> 63</td><td> 75</td><td>164</td><td> 98</td><td>138</td></tr>\n",
       "\t<tr><td>103</td><td> 77</td><td> 77</td><td>160</td><td>117</td><td>121</td></tr>\n",
       "\t<tr><td> 77</td><td> 68</td><td> 74</td><td>144</td><td> 71</td><td>153</td></tr>\n",
       "\t<tr><td> 66</td><td> 77</td><td> 68</td><td> 77</td><td> 82</td><td> 89</td></tr>\n",
       "\t<tr><td> 70</td><td> 70</td><td> 72</td><td>114</td><td> 93</td><td>122</td></tr>\n",
       "\t<tr><td> 75</td><td> 65</td><td> 71</td><td> 77</td><td> 70</td><td>109</td></tr>\n",
       "\t<tr><td> 91</td><td> 74</td><td> 93</td><td>118</td><td>115</td><td>150</td></tr>\n",
       "\t<tr><td> 66</td><td> 75</td><td> 73</td><td>170</td><td>147</td><td>121</td></tr>\n",
       "\t<tr><td> 75</td><td> 82</td><td> 76</td><td>153</td><td>132</td><td>115</td></tr>\n",
       "\t<tr><td> 74</td><td> 71</td><td> 66</td><td>143</td><td>105</td><td>100</td></tr>\n",
       "\t<tr><td> 76</td><td> 70</td><td> 64</td><td>114</td><td>113</td><td>129</td></tr>\n",
       "\t<tr><td> 74</td><td> 90</td><td> 86</td><td> 73</td><td>106</td><td>116</td></tr>\n",
       "\t<tr><td> 74</td><td> 77</td><td> 80</td><td>116</td><td> 81</td><td> 77</td></tr>\n",
       "\t<tr><td> 67</td><td> 71</td><td> 69</td><td> 63</td><td> 87</td><td> 70</td></tr>\n",
       "\t<tr><td> 78</td><td> 75</td><td> 80</td><td>105</td><td>132</td><td> 80</td></tr>\n",
       "\t<tr><td> 64</td><td> 66</td><td> 71</td><td> 83</td><td> 94</td><td>133</td></tr>\n",
       "\t<tr><td> 71</td><td> 80</td><td> 76</td><td> 81</td><td> 87</td><td> 86</td></tr>\n",
       "\t<tr><td> 63</td><td> 75</td><td> 73</td><td>120</td><td> 89</td><td> 59</td></tr>\n",
       "\t<tr><td> 90</td><td>103</td><td> 74</td><td>107</td><td>109</td><td>101</td></tr>\n",
       "\t<tr><td> 60</td><td> 76</td><td> 61</td><td> 99</td><td>111</td><td> 98</td></tr>\n",
       "\t<tr><td> 48</td><td> 77</td><td> 75</td><td>113</td><td>124</td><td> 97</td></tr>\n",
       "\t<tr><td> 66</td><td> 93</td><td> 97</td><td>136</td><td>112</td><td>122</td></tr>\n",
       "\t<tr><td> 74</td><td> 70</td><td> 76</td><td>109</td><td> 88</td><td>105</td></tr>\n",
       "\t<tr><td> 60</td><td> 74</td><td> 71</td><td> 72</td><td> 90</td><td> 71</td></tr>\n",
       "\t<tr><td> 63</td><td> 75</td><td> 66</td><td>130</td><td>101</td><td> 90</td></tr>\n",
       "\t<tr><td> 66</td><td> 80</td><td> 86</td><td>130</td><td>117</td><td>144</td></tr>\n",
       "\t<tr><td> 77</td><td> 67</td><td> 74</td><td> 83</td><td> 92</td><td>107</td></tr>\n",
       "\t<tr><td> 70</td><td> 67</td><td>100</td><td>150</td><td>142</td><td>146</td></tr>\n",
       "\t<tr><td> 73</td><td> 76</td><td> 81</td><td>119</td><td>120</td><td>119</td></tr>\n",
       "\t<tr><td> 78</td><td> 90</td><td> 77</td><td>122</td><td>155</td><td>149</td></tr>\n",
       "\t<tr><td> 73</td><td> 68</td><td> 80</td><td>102</td><td> 90</td><td>122</td></tr>\n",
       "\t<tr><td> 72</td><td> 83</td><td> 68</td><td>104</td><td> 69</td><td> 96</td></tr>\n",
       "\t<tr><td> 65</td><td> 60</td><td> 70</td><td>119</td><td> 94</td><td> 89</td></tr>\n",
       "\t<tr><td> 52</td><td> 70</td><td> 76</td><td> 92</td><td> 94</td><td>100</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A data.frame: 49 × 6\n",
       "\\begin{tabular}{llllll}\n",
       " x1 & x2 & x3 & y1 & y2 & y3\\\\\n",
       " <int> & <int> & <int> & <int> & <int> & <int>\\\\\n",
       "\\hline\n",
       "\t  60 &  69 &  62 &  97 &  69 &  98\\\\\n",
       "\t  56 &  53 &  84 & 103 &  78 & 107\\\\\n",
       "\t  80 &  69 &  76 &  66 &  99 & 130\\\\\n",
       "\t  55 &  80 &  90 &  80 &  85 & 114\\\\\n",
       "\t  62 &  75 &  68 & 116 & 130 &  91\\\\\n",
       "\t  74 &  64 &  70 & 109 & 101 & 103\\\\\n",
       "\t  64 &  71 &  66 &  77 & 102 & 130\\\\\n",
       "\t  73 &  70 &  64 & 115 & 110 & 109\\\\\n",
       "\t  68 &  67 &  75 &  76 &  85 & 119\\\\\n",
       "\t  69 &  82 &  74 &  72 & 133 & 127\\\\\n",
       "\t  60 &  67 &  61 & 130 & 134 & 121\\\\\n",
       "\t  70 &  74 &  78 & 150 & 158 & 100\\\\\n",
       "\t  66 &  74 &  78 & 150 & 131 & 142\\\\\n",
       "\t  83 &  70 &  74 &  99 &  98 & 105\\\\\n",
       "\t  68 &  66 &  90 & 119 &  85 & 109\\\\\n",
       "\t  78 &  63 &  75 & 164 &  98 & 138\\\\\n",
       "\t 103 &  77 &  77 & 160 & 117 & 121\\\\\n",
       "\t  77 &  68 &  74 & 144 &  71 & 153\\\\\n",
       "\t  66 &  77 &  68 &  77 &  82 &  89\\\\\n",
       "\t  70 &  70 &  72 & 114 &  93 & 122\\\\\n",
       "\t  75 &  65 &  71 &  77 &  70 & 109\\\\\n",
       "\t  91 &  74 &  93 & 118 & 115 & 150\\\\\n",
       "\t  66 &  75 &  73 & 170 & 147 & 121\\\\\n",
       "\t  75 &  82 &  76 & 153 & 132 & 115\\\\\n",
       "\t  74 &  71 &  66 & 143 & 105 & 100\\\\\n",
       "\t  76 &  70 &  64 & 114 & 113 & 129\\\\\n",
       "\t  74 &  90 &  86 &  73 & 106 & 116\\\\\n",
       "\t  74 &  77 &  80 & 116 &  81 &  77\\\\\n",
       "\t  67 &  71 &  69 &  63 &  87 &  70\\\\\n",
       "\t  78 &  75 &  80 & 105 & 132 &  80\\\\\n",
       "\t  64 &  66 &  71 &  83 &  94 & 133\\\\\n",
       "\t  71 &  80 &  76 &  81 &  87 &  86\\\\\n",
       "\t  63 &  75 &  73 & 120 &  89 &  59\\\\\n",
       "\t  90 & 103 &  74 & 107 & 109 & 101\\\\\n",
       "\t  60 &  76 &  61 &  99 & 111 &  98\\\\\n",
       "\t  48 &  77 &  75 & 113 & 124 &  97\\\\\n",
       "\t  66 &  93 &  97 & 136 & 112 & 122\\\\\n",
       "\t  74 &  70 &  76 & 109 &  88 & 105\\\\\n",
       "\t  60 &  74 &  71 &  72 &  90 &  71\\\\\n",
       "\t  63 &  75 &  66 & 130 & 101 &  90\\\\\n",
       "\t  66 &  80 &  86 & 130 & 117 & 144\\\\\n",
       "\t  77 &  67 &  74 &  83 &  92 & 107\\\\\n",
       "\t  70 &  67 & 100 & 150 & 142 & 146\\\\\n",
       "\t  73 &  76 &  81 & 119 & 120 & 119\\\\\n",
       "\t  78 &  90 &  77 & 122 & 155 & 149\\\\\n",
       "\t  73 &  68 &  80 & 102 &  90 & 122\\\\\n",
       "\t  72 &  83 &  68 & 104 &  69 &  96\\\\\n",
       "\t  65 &  60 &  70 & 119 &  94 &  89\\\\\n",
       "\t  52 &  70 &  76 &  92 &  94 & 100\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A data.frame: 49 × 6\n",
       "\n",
       "| x1 &lt;int&gt; | x2 &lt;int&gt; | x3 &lt;int&gt; | y1 &lt;int&gt; | y2 &lt;int&gt; | y3 &lt;int&gt; |\n",
       "|---|---|---|---|---|---|\n",
       "|  60 |  69 |  62 |  97 |  69 |  98 |\n",
       "|  56 |  53 |  84 | 103 |  78 | 107 |\n",
       "|  80 |  69 |  76 |  66 |  99 | 130 |\n",
       "|  55 |  80 |  90 |  80 |  85 | 114 |\n",
       "|  62 |  75 |  68 | 116 | 130 |  91 |\n",
       "|  74 |  64 |  70 | 109 | 101 | 103 |\n",
       "|  64 |  71 |  66 |  77 | 102 | 130 |\n",
       "|  73 |  70 |  64 | 115 | 110 | 109 |\n",
       "|  68 |  67 |  75 |  76 |  85 | 119 |\n",
       "|  69 |  82 |  74 |  72 | 133 | 127 |\n",
       "|  60 |  67 |  61 | 130 | 134 | 121 |\n",
       "|  70 |  74 |  78 | 150 | 158 | 100 |\n",
       "|  66 |  74 |  78 | 150 | 131 | 142 |\n",
       "|  83 |  70 |  74 |  99 |  98 | 105 |\n",
       "|  68 |  66 |  90 | 119 |  85 | 109 |\n",
       "|  78 |  63 |  75 | 164 |  98 | 138 |\n",
       "| 103 |  77 |  77 | 160 | 117 | 121 |\n",
       "|  77 |  68 |  74 | 144 |  71 | 153 |\n",
       "|  66 |  77 |  68 |  77 |  82 |  89 |\n",
       "|  70 |  70 |  72 | 114 |  93 | 122 |\n",
       "|  75 |  65 |  71 |  77 |  70 | 109 |\n",
       "|  91 |  74 |  93 | 118 | 115 | 150 |\n",
       "|  66 |  75 |  73 | 170 | 147 | 121 |\n",
       "|  75 |  82 |  76 | 153 | 132 | 115 |\n",
       "|  74 |  71 |  66 | 143 | 105 | 100 |\n",
       "|  76 |  70 |  64 | 114 | 113 | 129 |\n",
       "|  74 |  90 |  86 |  73 | 106 | 116 |\n",
       "|  74 |  77 |  80 | 116 |  81 |  77 |\n",
       "|  67 |  71 |  69 |  63 |  87 |  70 |\n",
       "|  78 |  75 |  80 | 105 | 132 |  80 |\n",
       "|  64 |  66 |  71 |  83 |  94 | 133 |\n",
       "|  71 |  80 |  76 |  81 |  87 |  86 |\n",
       "|  63 |  75 |  73 | 120 |  89 |  59 |\n",
       "|  90 | 103 |  74 | 107 | 109 | 101 |\n",
       "|  60 |  76 |  61 |  99 | 111 |  98 |\n",
       "|  48 |  77 |  75 | 113 | 124 |  97 |\n",
       "|  66 |  93 |  97 | 136 | 112 | 122 |\n",
       "|  74 |  70 |  76 | 109 |  88 | 105 |\n",
       "|  60 |  74 |  71 |  72 |  90 |  71 |\n",
       "|  63 |  75 |  66 | 130 | 101 |  90 |\n",
       "|  66 |  80 |  86 | 130 | 117 | 144 |\n",
       "|  77 |  67 |  74 |  83 |  92 | 107 |\n",
       "|  70 |  67 | 100 | 150 | 142 | 146 |\n",
       "|  73 |  76 |  81 | 119 | 120 | 119 |\n",
       "|  78 |  90 |  77 | 122 | 155 | 149 |\n",
       "|  73 |  68 |  80 | 102 |  90 | 122 |\n",
       "|  72 |  83 |  68 | 104 |  69 |  96 |\n",
       "|  65 |  60 |  70 | 119 |  94 |  89 |\n",
       "|  52 |  70 |  76 |  92 |  94 | 100 |\n",
       "\n"
      ],
      "text/plain": [
       "   x1  x2  x3  y1  y2  y3 \n",
       "1   60  69  62  97  69  98\n",
       "2   56  53  84 103  78 107\n",
       "3   80  69  76  66  99 130\n",
       "4   55  80  90  80  85 114\n",
       "5   62  75  68 116 130  91\n",
       "6   74  64  70 109 101 103\n",
       "7   64  71  66  77 102 130\n",
       "8   73  70  64 115 110 109\n",
       "9   68  67  75  76  85 119\n",
       "10  69  82  74  72 133 127\n",
       "11  60  67  61 130 134 121\n",
       "12  70  74  78 150 158 100\n",
       "13  66  74  78 150 131 142\n",
       "14  83  70  74  99  98 105\n",
       "15  68  66  90 119  85 109\n",
       "16  78  63  75 164  98 138\n",
       "17 103  77  77 160 117 121\n",
       "18  77  68  74 144  71 153\n",
       "19  66  77  68  77  82  89\n",
       "20  70  70  72 114  93 122\n",
       "21  75  65  71  77  70 109\n",
       "22  91  74  93 118 115 150\n",
       "23  66  75  73 170 147 121\n",
       "24  75  82  76 153 132 115\n",
       "25  74  71  66 143 105 100\n",
       "26  76  70  64 114 113 129\n",
       "27  74  90  86  73 106 116\n",
       "28  74  77  80 116  81  77\n",
       "29  67  71  69  63  87  70\n",
       "30  78  75  80 105 132  80\n",
       "31  64  66  71  83  94 133\n",
       "32  71  80  76  81  87  86\n",
       "33  63  75  73 120  89  59\n",
       "34  90 103  74 107 109 101\n",
       "35  60  76  61  99 111  98\n",
       "36  48  77  75 113 124  97\n",
       "37  66  93  97 136 112 122\n",
       "38  74  70  76 109  88 105\n",
       "39  60  74  71  72  90  71\n",
       "40  63  75  66 130 101  90\n",
       "41  66  80  86 130 117 144\n",
       "42  77  67  74  83  92 107\n",
       "43  70  67 100 150 142 146\n",
       "44  73  76  81 119 120 119\n",
       "45  78  90  77 122 155 149\n",
       "46  73  68  80 102  90 122\n",
       "47  72  83  68 104  69  96\n",
       "48  65  60  70 119  94  89\n",
       "49  52  70  76  92  94 100"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data <- read.csv(\"ex_4_6.csv\")[-1]; data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dental-hanging",
   "metadata": {},
   "source": [
    "1. 样本协方差矩阵 $S$："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fantastic-jersey",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 6 × 6 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>x1</th><th scope=col>x2</th><th scope=col>x3</th><th scope=col>y1</th><th scope=col>y2</th><th scope=col>y3</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>x1</th><td>97.33333</td><td>17.809524</td><td>12.02976</td><td> 58.720238</td><td> 22.35119</td><td> 61.529762</td></tr>\n",
       "\t<tr><th scope=row>x2</th><td>17.80952</td><td>74.579932</td><td>14.21854</td><td>  3.326105</td><td> 61.62160</td><td> -3.855867</td></tr>\n",
       "\t<tr><th scope=row>x3</th><td>12.02976</td><td>14.218537</td><td>76.96939</td><td> 41.667517</td><td> 31.21854</td><td> 66.109269</td></tr>\n",
       "\t<tr><th scope=row>y1</th><td>58.72024</td><td> 3.326105</td><td>41.66752</td><td>779.153912</td><td>310.15944</td><td>192.423469</td></tr>\n",
       "\t<tr><th scope=row>y2</th><td>22.35119</td><td>61.621599</td><td>31.21854</td><td>310.159439</td><td>510.07993</td><td>156.185799</td></tr>\n",
       "\t<tr><th scope=row>y3</th><td>61.52976</td><td>-3.855867</td><td>66.10927</td><td>192.423469</td><td>156.18580</td><td>485.332483</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 6 of type dbl\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & x1 & x2 & x3 & y1 & y2 & y3\\\\\n",
       "\\hline\n",
       "\tx1 & 97.33333 & 17.809524 & 12.02976 &  58.720238 &  22.35119 &  61.529762\\\\\n",
       "\tx2 & 17.80952 & 74.579932 & 14.21854 &   3.326105 &  61.62160 &  -3.855867\\\\\n",
       "\tx3 & 12.02976 & 14.218537 & 76.96939 &  41.667517 &  31.21854 &  66.109269\\\\\n",
       "\ty1 & 58.72024 &  3.326105 & 41.66752 & 779.153912 & 310.15944 & 192.423469\\\\\n",
       "\ty2 & 22.35119 & 61.621599 & 31.21854 & 310.159439 & 510.07993 & 156.185799\\\\\n",
       "\ty3 & 61.52976 & -3.855867 & 66.10927 & 192.423469 & 156.18580 & 485.332483\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 6 of type dbl\n",
       "\n",
       "| <!--/--> | x1 | x2 | x3 | y1 | y2 | y3 |\n",
       "|---|---|---|---|---|---|---|\n",
       "| x1 | 97.33333 | 17.809524 | 12.02976 |  58.720238 |  22.35119 |  61.529762 |\n",
       "| x2 | 17.80952 | 74.579932 | 14.21854 |   3.326105 |  61.62160 |  -3.855867 |\n",
       "| x3 | 12.02976 | 14.218537 | 76.96939 |  41.667517 |  31.21854 |  66.109269 |\n",
       "| y1 | 58.72024 |  3.326105 | 41.66752 | 779.153912 | 310.15944 | 192.423469 |\n",
       "| y2 | 22.35119 | 61.621599 | 31.21854 | 310.159439 | 510.07993 | 156.185799 |\n",
       "| y3 | 61.52976 | -3.855867 | 66.10927 | 192.423469 | 156.18580 | 485.332483 |\n",
       "\n"
      ],
      "text/plain": [
       "   x1       x2        x3       y1         y2        y3        \n",
       "x1 97.33333 17.809524 12.02976  58.720238  22.35119  61.529762\n",
       "x2 17.80952 74.579932 14.21854   3.326105  61.62160  -3.855867\n",
       "x3 12.02976 14.218537 76.96939  41.667517  31.21854  66.109269\n",
       "y1 58.72024  3.326105 41.66752 779.153912 310.15944 192.423469\n",
       "y2 22.35119 61.621599 31.21854 310.159439 510.07993 156.185799\n",
       "y3 61.52976 -3.855867 66.10927 192.423469 156.18580 485.332483"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "S <- cov(data); S"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "trying-guest",
   "metadata": {},
   "source": [
    "从协方差做 PCA："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "third-death",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Importance of components:\n",
       "                           Comp.1     Comp.2     Comp.3     Comp.4     Comp.5\n",
       "Standard deviation     32.7872275 19.7452189 17.5131159 9.88479688 8.28776305\n",
       "Proportion of Variance  0.5423404  0.1966919  0.1547353 0.04929446 0.03465271\n",
       "Cumulative Proportion   0.5423404  0.7390323  0.8937676 0.94306209 0.97771481\n",
       "                           Comp.6\n",
       "Standard deviation     6.64625362\n",
       "Proportion of Variance 0.02228519\n",
       "Cumulative Proportion  1.00000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca.cov <- princomp(data, cor=FALSE)\n",
    "summary(pca.cov)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fatal-horizontal",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.10623236"
      ],
      "text/latex": [
       "0.10623236"
      ],
      "text/markdown": [
       "0.10623236"
      ],
      "text/plain": [
       "[1] 0.1062324"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# sum last three proportion\n",
    "0.04929446+0.03465271+0.02228519"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "intended-stable",
   "metadata": {},
   "source": [
    "前三个主成分累积贡献率已占近 $89.37\\%$，第三主成分贡献率 $15.47\\%$，大于剩下三个成分的贡献率总和（$0.10623236$）。\n",
    "所以认为前三个主成分已包含原始数据的大量信息，所以保留前三个主成分即可。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "continent-peoples",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lXqs041GcP9k+XUvYYO3jupjuAk65PT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\nRK5CYII=",
      "text/plain": [
       "Plot with title “pca.cov”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(pca.cov, type=\"lines\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "minus-monday",
   "metadata": {},
   "source": [
    "同时，前三个主成分所占方差较大，这也证明了上述结论。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "pretty-policy",
   "metadata": {},
   "source": [
    "2. 样本相关系数矩阵 $R$："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "becoming-bridal",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 6 × 6 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>x1</th><th scope=col>x2</th><th scope=col>x3</th><th scope=col>y1</th><th scope=col>y2</th><th scope=col>y3</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>x1</th><td>1.0000000</td><td> 0.20903091</td><td>0.1389848</td><td>0.21322856</td><td>0.1003115</td><td> 0.28309667</td></tr>\n",
       "\t<tr><th scope=row>x2</th><td>0.2090309</td><td> 1.00000000</td><td>0.1876657</td><td>0.01379791</td><td>0.3159387</td><td>-0.02026709</td></tr>\n",
       "\t<tr><th scope=row>x3</th><td>0.1389848</td><td> 0.18766571</td><td>1.0000000</td><td>0.17014805</td><td>0.1575558</td><td> 0.34204532</td></tr>\n",
       "\t<tr><th scope=row>y1</th><td>0.2132286</td><td> 0.01379791</td><td>0.1701481</td><td>1.00000000</td><td>0.4919877</td><td> 0.31291525</td></tr>\n",
       "\t<tr><th scope=row>y2</th><td>0.1003115</td><td> 0.31593872</td><td>0.1575558</td><td>0.49198771</td><td>1.0000000</td><td> 0.31390826</td></tr>\n",
       "\t<tr><th scope=row>y3</th><td>0.2830967</td><td>-0.02026709</td><td>0.3420453</td><td>0.31291525</td><td>0.3139083</td><td> 1.00000000</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 6 × 6 of type dbl\n",
       "\\begin{tabular}{r|llllll}\n",
       "  & x1 & x2 & x3 & y1 & y2 & y3\\\\\n",
       "\\hline\n",
       "\tx1 & 1.0000000 &  0.20903091 & 0.1389848 & 0.21322856 & 0.1003115 &  0.28309667\\\\\n",
       "\tx2 & 0.2090309 &  1.00000000 & 0.1876657 & 0.01379791 & 0.3159387 & -0.02026709\\\\\n",
       "\tx3 & 0.1389848 &  0.18766571 & 1.0000000 & 0.17014805 & 0.1575558 &  0.34204532\\\\\n",
       "\ty1 & 0.2132286 &  0.01379791 & 0.1701481 & 1.00000000 & 0.4919877 &  0.31291525\\\\\n",
       "\ty2 & 0.1003115 &  0.31593872 & 0.1575558 & 0.49198771 & 1.0000000 &  0.31390826\\\\\n",
       "\ty3 & 0.2830967 & -0.02026709 & 0.3420453 & 0.31291525 & 0.3139083 &  1.00000000\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 6 × 6 of type dbl\n",
       "\n",
       "| <!--/--> | x1 | x2 | x3 | y1 | y2 | y3 |\n",
       "|---|---|---|---|---|---|---|\n",
       "| x1 | 1.0000000 |  0.20903091 | 0.1389848 | 0.21322856 | 0.1003115 |  0.28309667 |\n",
       "| x2 | 0.2090309 |  1.00000000 | 0.1876657 | 0.01379791 | 0.3159387 | -0.02026709 |\n",
       "| x3 | 0.1389848 |  0.18766571 | 1.0000000 | 0.17014805 | 0.1575558 |  0.34204532 |\n",
       "| y1 | 0.2132286 |  0.01379791 | 0.1701481 | 1.00000000 | 0.4919877 |  0.31291525 |\n",
       "| y2 | 0.1003115 |  0.31593872 | 0.1575558 | 0.49198771 | 1.0000000 |  0.31390826 |\n",
       "| y3 | 0.2830967 | -0.02026709 | 0.3420453 | 0.31291525 | 0.3139083 |  1.00000000 |\n",
       "\n"
      ],
      "text/plain": [
       "   x1        x2          x3        y1         y2        y3         \n",
       "x1 1.0000000  0.20903091 0.1389848 0.21322856 0.1003115  0.28309667\n",
       "x2 0.2090309  1.00000000 0.1876657 0.01379791 0.3159387 -0.02026709\n",
       "x3 0.1389848  0.18766571 1.0000000 0.17014805 0.1575558  0.34204532\n",
       "y1 0.2132286  0.01379791 0.1701481 1.00000000 0.4919877  0.31291525\n",
       "y2 0.1003115  0.31593872 0.1575558 0.49198771 1.0000000  0.31390826\n",
       "y3 0.2830967 -0.02026709 0.3420453 0.31291525 0.3139083  1.00000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "R <- cor(data); R"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "unexpected-martin",
   "metadata": {},
   "source": [
    "从相关系数做 PCA："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "dominican-legislature",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Importance of components:\n",
       "                          Comp.1    Comp.2    Comp.3    Comp.4     Comp.5\n",
       "Standard deviation     1.4565616 1.0412531 0.9989804 0.9336374 0.76120123\n",
       "Proportion of Variance 0.3535953 0.1807013 0.1663270 0.1452798 0.09657122\n",
       "Cumulative Proportion  0.3535953 0.5342966 0.7006236 0.8459034 0.94247458\n",
       "                           Comp.6\n",
       "Standard deviation     0.58749684\n",
       "Proportion of Variance 0.05752542\n",
       "Cumulative Proportion  1.00000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca.cor <- princomp(data, cor=TRUE)\n",
    "summary(pca.cor)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "tracked-cattle",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.15409664"
      ],
      "text/latex": [
       "0.15409664"
      ],
      "text/markdown": [
       "0.15409664"
      ],
      "text/plain": [
       "[1] 0.1540966"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "0.09657122+0.05752542"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "configured-plymouth",
   "metadata": {},
   "source": [
    "从以结果可看出前四个主成分累积贡献率已占 $84.59\\%$ 且第四个主成分的贡献率为 $0.1452798$，与剩下两个成分的总和（$0.15409664$）差不多，所以保留前四个主成分即可。\n",
    "\n",
    "从方差来看，也可以佐证之。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "continuous-champagne",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BAgQIAAAQIECBAgQIAAAQIECBAgQIAA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\nIECAAAECBAgQIECAAIHVCPwv7GMV6IROb8kAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title “pca.cor”"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot(pca.cor, type=\"lines\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "increasing-shipping",
   "metadata": {},
   "source": [
    "相较之下，我认为使用基于样本协方差矩阵 $S$ 的主成分分析结果更好。\n",
    "基于 $S$ 的前 3 个主成分累积贡献就超过了 $89.37\\%$，\n",
    "而基于 $R$ 前 4 个主成分累积贡献才不到 $84.59\\%$，\n",
    "显然使用基于 $S$ 的分析更好。\n",
    "\n",
    "同时考虑到具体的问题，空腹和摄入食糖的测量数据等量纲，无需进行标准化，这种数据基于协方差矩阵 $S$ 的分析结果更为合理。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "4.0.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
